There are numerous clinical situations where repeated tomographic acquisitions are prescribed. For example, in lung cancer treatment such scans are used both for diagnostics as well as image-guided procedures. Specifically, repeated surveillance scans are used diagnostically to monitor nodule size over the course of treatment. Similarly, Computed Tomography (CT) may be used in a cine mode to guide a biopsy needle, wherein the cine mode provides a series of rapidly recorded multiple image volumes taken at sequential cycles of time. In both cases, there tends to be substantial similarity between the images in the acquisition sequence. Such similarities have previously been exploited in reconstruction methods as image priors for subsequent reconstructions from sparse data acquisitions, most notably in prior image constrained compressed sensing (PICCS) reconstructions. These sparse acquisitions can be angularly undersampled, limited arcs, and/or highly truncated, providing the opportunity for significant dose reductions or decreased acquisition times. Analogous acquisition and reconstruction problems exist on other imaging modalities (e.g. magnetic resonance imaging).
PICCS reconstruction relies on compressed sensing norms that are well suited to ill-posed problems due to their ability to enforce sparsity in reconstructions. The total variation norm (or L1 norm) can be one particular choice. The total variation norm is a method for reducing noise in images while preserving the representation of edges. Typically, the method is performed by applying a so-called sparsifying transformation to the estimated imagery, like a spatial gradient, if the underlying image itself is not already a sparse entity. When prior images are utilized in a reconstruction, one would expect that the difference between a registered prior image and the new reconstruction is sparse, having significant values only in regions of change. In some cases, additional sparsifying transforms are applied even though this difference may already be sparse. If the prior image is not well-registered, one would expect there to be more significant differences, and the prior image therefore would have decreased utility. As such, PICCS approaches that include an initial prior image registration are known in the art.
However, there are drawbacks with the known methods of image reconstruction. For example, while there are modifications to PICCS that accommodate misregistration, such techniques are applied as a pre-processing step as opposed to simultaneous processing that would leverage intermediate reconstructions to improve the registration, perhaps as part of an iterative procedure. Another potential issue with such compressed sensing reconstructions is that they tend to adopt a simplified forward model and no noise model. This is usually required in order to apply a linear constraint on a compressing sensing objective. Likelihood-based approaches are also known. However, while likelihood methods can make use of fairly sophisticated forward models, they have not incorporated prior images in their objective function.
Each of the foregoing approaches is used to minimize a compressed sensing or total variation type norm on the imagery subject to a constraint that observed data matches the reprojected image estimate. This is typically applied as a linear constraint matching the log-transformed data with the reprojected estimate. While this approach is attractive since it strictly enforces the data match criterion, it does not recognize that different measurements may contain different information content. For example, it is common to presume that x-ray measurements follow a Poisson noise distribution. As such, the noise variance can be substantially space-variant with different rays possessing very different signal-to-noise ratios. In fact, it appears that PICCS may presume some kind of noise model that is homoscedastic having the same variance in the log-transformed measurement space.